Simultaneous Multiple Response Regression and Inverse Covariance Matrix Estimation via Penalized Gaussian Maximum Likelihood.
Simultaneous Multiple Response Regression and Inverse Covariance Matrix Estimation via Penalized Gaussian Maximum Likelihood.
复制标题
DOI：
10.1016/j.jmva.2012.03.013
复制
发表时间：
2012-10-01
影响因子：
1.6
通讯作者：
Liu, Yufeng
中科院分区：
文献类型：
--
作者：
Lee, Wonyul;Liu, Yufeng
多元回归是解决实际问题的常用统计工具。许多多元回归技术都是针对单变量响应情况而设计的。对于具有多个响应变量的问题，一种常见的方法是对每个响应变量分别应用单变量响应回归技术。单变量响应方法虽然简单易行，但忽略了响应变量之间的联合信息。在本文中，我们提出了三种利用响应变量间联合信息的新方法。所有方法都在带有加权L1正则化的惩罚似然框架内。所提出的方法提供了给定解释变量的响应向量的条件逆协差阵的稀疏估计以及回归参数的稀疏估计。第一种方法是用插件估计的逆协方差矩阵估计回归系数，第二种方法是用插件估计的回归参数估计逆协方差矩阵。我们的第三种方法是同时估计两者。研究了这些方法的渐近性质。数值算例表明，该方法在预测、变量选择以及逆协方差矩阵估计等方面具有较强的竞争力。
Multivariate regression is a common statistical tool for practical problems. Many multivariate regression techniques are designed for univariate response cases. For problems with multiple response variables available, one common approach is to apply the univariate response regression technique separately on each response variable. Although it is simple and popular, the univariate response approach ignores the joint information among response variables. In this paper, we propose three new methods for utilizing joint information among response variables. All methods are in a penalized likelihood framework with weighted L1 regularization. The proposed methods provide sparse estimators of conditional inverse co-variance matrix of response vector given explanatory variables as well as sparse estimators of regression parameters. Our first approach is to estimate the regression coefficients with plug-in estimated inverse covariance matrices, and our second approach is to estimate the inverse covariance matrix with plug-in estimated regression parameters. Our third approach is to estimate both simultaneously. Asymptotic properties of these methods are explored. Our numerical examples demonstrate that the proposed methods perform competitively in terms of prediction, variable selection, as well as inverse covariance matrix estimation.
登录
查看更多内容
DOI：
10.1198/jcgs.2010.09188
发表时间：
2010
期刊：
Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
影响因子：
--
作者：
Rothman AJ;Levina E;Zhu J
通讯作者：
Zhu J
影响因子：
3.7
作者：
Peng J;Wang P;Zhou N;Zhu J
通讯作者：
Zhu J
影响因子：
2.1
作者：
Osborne, MR;Presnell, B;Turlach, BA
通讯作者：
Turlach, BA
影响因子：
64.8
作者：
Chin, L.;Meyerson, M.;Aldape, K.;Bigner, D.;Mikkelsen, T.;VandenBerg, S.;Kahn, A.;Penny, R.;Ferguson, M. L.;Gerhard, D. S.;Getz, G.;Brennan, C.;Taylor, B. S.;Winckler, W.;Park, P.;Ladanyi, M.;Hoadley, K. A.;Verhaak, R. G. W.;Hayes, D. N.;Spellman, Paul T.;Absher, D.;Weir, B. A.;Ding, L.;Wheeler, D.;Lawrence, M. S.;Cibulskis, K.;Mardis, E.;Zhang, Jinghui;Wilson, R. K.;Donehower, L.;Wheeler, D. A.;Purdom, E.;Wallis, J.;Laird, P. W.;Herman, J. G.;Schuebel, K. E.;Weisenberger, D. J.;Baylin, S. B.;Schultz, N.;Yao, Jun;Wiedemeyer, R.;Weinstein, J.;Sander, C.;Gibbs, R. A.;Gray, J.;Kucherlapati, R.;Lander, E. S.;Myers, R. M.;Perou, C. M.;McLendon, Roger;Friedman, Allan;Van Meir, Erwin G;Brat, Daniel J;Mastrogianakis, Gena Marie;Olson, Jeffrey J;Lehman, Norman;Yung, W. K. Alfred;Bogler, Oliver;Berger, Mitchel;Prados, Michael;Muzny, Donna;Morgan, Margaret;Scherer, Steve;Sabo, Aniko;Nazareth, Lynn;Lewis, Lora;Hall, Otis;Zhu, Yiming;Ren, Yanru;Alvi, Omar;Yao, Jiqiang;Hawes, Alicia;Jhangiani, Shalini;Fowler, Gerald;San Lucas, Anthony;Kovar, Christie;Cree, Andrew;Dinh, Huyen;Santibanez, Jireh;Joshi, Vandita;Gonzalez-Garay, Manuel L.;Miller, Christopher A.;Milosavljevic, Aleksandar;Sougnez, Carrie;Fennell, Tim;Mahan, Scott;Wilkinson, Jane;Ziaugra, Liuda;Onofrio, Robert;Bloom, Toby;Nicol, Rob;Ardlie, Kristin;Baldwin, Jennifer;Gabriel, Stacey;Fulton, Robert S.;McLellan, Michael D.;Larson, David E.;Shi, Xiaoqi;Abbott, Rachel;Fulton, Lucinda;Chen, Ken;Koboldt, Daniel C.;Wendl, Michael C.;Meyer, Rick;Tang, Yuzhu;Lin, Ling;Osborne, John R.;Dunford-Shore, Brian H.;Miner, Tracie L.;Delehaunty, Kim;Markovic, Chris;Swift, Gary;Courtney, William;Pohl, Craig;Abbott, Scott;Hawkins, Amy;Leong, Shin;Haipek, Carrie;Schmidt, Heather;Wiechert, Maddy;Vickery, Tammi;Scott, Sacha;Dooling, David J.;Chinwalla, Asif;Weinstock, George M.;O'Kelly, Michael;Robinson, Jim;Alexe, Gabriele;Beroukhim, Rameen;Carter, Scott;Chiang, Derek;Gould, Josh;Gupta, Supriya;Korn, Josh;Mermel, Craig;Mesirov, Jill;Monti, Stefano;Nguyen, Huy;Parkin, Melissa;Reich, Michael;Stransky, Nicolas;Garraway, Levi;Golub, Todd;Protopopov, Alexei;Perna, Ilana;Aronson, Sandy;Sathiamoorthy, Narayan;Ren, Georgia;Kim, Hyunsoo;Kong, Sek Won;Xiao, Yonghong;Kohane, Isaac S.;Seidman, Jon;Cope, Leslie;Pan, Fei;Van Den Berg, David;Van Neste, Leander;Yi, Joo Mi;Li, Jun Z.;Southwick, Audrey;Brady, Shannon;Aggarwal, Amita;Chung, Tisha;Sherlock, Gavin;Brooks, James D.;Jakkula, Lakshmi R.;Lapuk, Anna V.;Marr, Henry;Dorton, Shannon;Choi, Yoon Gi;Han, Ju;Ray, Amrita;Wang, Victoria;Durinck, Steffen;Robinson, Mark;Wang, Nicholas J.;Vranizan, Karen;Peng, Vivian;Van Name, Eric;Fontenay, Gerald V.;Ngai, John;Conboy, John G.;Parvin, Bahram;Feiler, Heidi S.;Speed, Terence P.;Socci, Nicholas D.;Olshen, Adam;Lash, Alex;Reva, Boris;Antipin, Yevgeniy;Stukalov, Alexey;Gross, Benjamin;Cerami, Ethan;Wang, Wei Qing;Qin, Li-Xuan;Seshan, Venkatraman E.;Villafania, Liliana;Cavatore, Magali;Borsu, Laetitia;Viale, Agnes;Gerald, William;Topal, Michael D.;Qi, Yuan;Balu, Sai;Shi, Yan;Wu, George;Bittner, Michael;Shelton, Troy;Lenkiewicz, Elizabeth;Morris, Scott;Beasley, Debbie;Sanders, Sheri;Sfeir, Robert;Chen, Jessica;Nassau, David;Feng, Larry;Hickey, Erin;Schaefer, Carl;Madhavan, Subha;Buetow, Ken;Barker, Anna;Vockley, Joseph;Compton, Carolyn;Vaught, Jim;Fielding, Peter;Collins, Francis;Good, Peter;Guyer, Mark;Ozenberger, Brad;Peterson, Jane;Thomson, Elizabeth
通讯作者：
Thomson, Elizabeth
DOI：
10.1111/j.1467-9868.2007.00627.x
发表时间：
2008-01-01
影响因子：
5.8
作者：
Meier, Lukas;van de Geer, Sara A.;Buhlmann, Peter
通讯作者：
Buhlmann, Peter